Question

(b) Radon is a naturally occurring radioactive gas found in the ground and in building materials. It is easily inhaled and emits α particles when it decays. Cumulative radon exposure is a significant risk factor for lung cancer. a. Calculate the density of radon at 298 K and 1 atm of pressure. b. Are radon concentrations likely to be greater in the basement or on the top floor of a building

Answer 1

d = 9.08 Kg/m³

Radon concentrations are greater in the basement.

Step-by-step explanation:

To find the density of radon, we need to use the ideal gas law:

`PV=nRT` (1)

where, P: pressure, V: volume, n: moles of gas, T: absolute temperature y R: ideal gas constant.

Knowing that the number of moles is:

`n= (m)/(M)` (2)

where m: mass of gas, and M: molar mass of gas,

Then, we can replace the number of moles into equation (1):

`PV= (m)/(M) \cdot RT`

The density of the gas is giving by:

`d= (m)/(V)` (3)

where: m: mass and V: volume of gas

Now, we can calculate the density of Radon:

`d=(m)/(V)= (PM)/(RT)`

`d=(1 \cdot 222)/(0.082 \cdot 298)`

`d= 9.08 (g)/(L)} = 9.08 (Kg)/(m^(3))}`

The ²²²Rn is produced by the decay of radium isotope ²²⁶Ra from the uranium-238 decay chain. Uranium is present in ground minerals, from which the radon gas can emerge and then accumulate in basements of buildings, due to its high density. Hence, because of its high density compared to the air (about 1.225 Kg/m³), radon concentrations are likely to be greater in the basement than on the top floor of a building.

Answer 2

a. the density of radon = 0.0908g/m3

b. radon gas concentration will be greater on top of the building than than basement.

Step-by-step explanation:

the solution to this question can be gotten from ideal gas law.

the ideal gas law is given by :

PV = nRT

where

P = atmospheric pressure in atm = 1 atm

V = volume in m3

n = number of moles

R = the gas constant.

T = temperature in kelvin = 298K

the gas constant R is given as 8.3145J.mol-1.K-1 or 8.2057m3.atm/mol.K.

n= mass of gas divided by molecular mass of gas = m/MM

PV = nRT

V/n = RT/P

V/m =RT/MM.P

density = m/V = (MM*P)/(RT)

the molecular mass of Radon is a constant which is 222g/mol

the density of radon = (222*1)/(8.2057 * 298)

= 0.0908g/m3

b. radon gas concentration will be greater on top of the building than than basement. radon concentration increases as height increases. also radon concentration increases greatly in the afternoon and evening and decreases in the morning. this means temperature affect the concentration.